Brain Teaser
A teacher writes an integer less than 50,000 on the blackboard.
One student states that the number is a multiple of 2; a second student
states that the number is a multiple of 3; and so on until the twelfth
student states that it is a multiple of 13.
The teacher remarks that all except two of the students were right and,
moreover, that the two were wrong spoke one after the other.
What was the number that the teacher wrote on the blackboard?
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The answer is 25,740
It's divisible by all but 7 & 8